The Ideal Gas Law is based on the assumptions that gases are composed of point masses that undergo perfectly elastic collisions; real gases deviate from those approximations, however, particularly in low temperature or high pressure conditions.
The van der Waals Equation and P-V Isotherms
Derived by Johannes Diderik van der Waals in 1873, the van der Waals equation modifies the Ideal Gas Law; it predicts the properties of real gases by describing particles of non-zero volume governed by pairwise attractive forces. This equation of state is presented as:
(P+an2V2)(V−nb)=nRT
where P is the pressure, V is the volume, R is the universal gas constant, and T is the absolute temperature. Isotherm (plots of pressure versus volume at constant temperature) can be produced using the van der Waals model.